Recently, one novel approach to calculate DC conductivities was proposed in [1]}, [2]}. Based on the idea of the membrane paradigm, this method provides an effective way to derive the DC transports from the data of black horizon. So once given a charged black hole solution in AdS space, one can calculate the DC electrical conductivities in terms of matter fields on the horizon. Furthermore, in [3]}, [4]}, the authors consider the dyonic black holes and get the Hall conductivities. Inspired by these work, various models have been discussed in [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}.
On the other hand, for a specific class of black hole, there is an interesting property named "attractor mechanism" [12]}. It states that the magnitude of a matter field obtains some values on the black hole horizon, which are dependent only upon the electric and magnetic charges of the black hole. In other words, the configuration of a black hole near horizon depends only on the electric and magnetic charges of the black hole and not on the asymptotic values of other matter fields. Thus it is very natural to think about whether one can use the attractor mechanism to calculate the DC conductivities without knowing the full black hole solutions. Following the spirit of the above discussions, in the work [13]}, the authors employ the Sen's entropy function method to get the horizon data and conductivities for Einstein-Maxwell-Dilaton theory. In addition, the Einstein-Maxwell theory with topological Maxwell term was discussed in [14]}, [15]}.
